User:Bdm
From Calendar Wiki
[edit] Four Basic Principles
Solar calendars for Earth can satisfy no more than three of the following four properties:
- Accuracy - The calendar tracks the seasons accurately.
- 7-day week - The week has exactly 7 days and the weekday cycle is uninterrupted in perpetuity.
- Leap Day - The intercalation is performed by inserting no more than one leap day.
- Perpetual - The calendar always starts on the same day of the week.
Solar calendars for Earth cannot simultaneously satisfy all of these four properties. Instead, they must all satisfy no more than three and sacrifice the fourth.
- Examples
- The Gregorian calendar adheres to principle 1 (accurate), 2 (7-day week) and 3 (one leap day) - it is not perpetual
- The Symmetry454 Calendar calendar adheres to principles 1 (accurate), 2 (7-day week) and 4 (perpetual) - intercalation inserts 7 days
- The World Calendar adheres to principle 1 (accurate), 3 (one leap day) and 4 (perpetual) - uses one or two "blank" days that interrupt the week
- A hypothetical 364-day calendar would adhere to 2 (7-day week), 3 (no more than one leap day) and 4 (perpetual) but would not be accurate.
[edit] Gregorian Calendar
- Is common or leap (2 permutations)
- Can start on any day of the week (7 permutations)
- Easter can be in any of five weeks (5 permutations)
| Week 1 | March 22 to March 28 |
|---|---|
| Week 2 | March 29 to April 4 |
| Week 3 | April 5 to April 11 |
| Week 4 | April 12 to April 18 |
| Week 5 | April 19 to April 25 |
This gives a total of 70 permutations (2 × 7 × 5). A year layout can be specified by specifying common or leap, naming the starting day, and which week Easter falls in of the possible Easter weeks (week 1 to week 5). For example, 2008 is a Leap Year beginning on Tuesday with Easter in week 1 (March 23). A more concise way of naming this layout would be Leap/Tuesday/1, or LTu1.
Particular year layouts can only be followed by certain other year layouts. For example, Leap years can only be followed by Common years starting two days later in the weekday cycle than the Leap year, Common years can only be followed by Common years or Leap years starting one day later in the weekday cycle, and Easter weeks have similar restrictions.
